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Simplifying Ln(5x + 1) + -1lnx = 3 Reorder the terms: nL(1 + 5x) + -1lnx = 3 (1 * nL + 5x * nL) + -1lnx = 3 (1nL + 5nxL) + -1lnx = 3 Reorder the terms: -1lnx + 1nL + 5nxL = 3 Solving -1lnx + 1nL + 5nxL = 3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1nL' to each side of the equation. -1lnx + 1nL + -1nL + 5nxL = 3 + -1nL Combine like terms: 1nL + -1nL = 0 -1lnx + 0 + 5nxL = 3 + -1nL -1lnx + 5nxL = 3 + -1nL Add '-5nxL' to each side of the equation. -1lnx + 5nxL + -5nxL = 3 + -1nL + -5nxL Combine like terms: 5nxL + -5nxL = 0 -1lnx + 0 = 3 + -1nL + -5nxL -1lnx = 3 + -1nL + -5nxL Divide each side by '-1nx'. l = -3n-1x-1 + x-1L + 5L Simplifying l = -3n-1x-1 + x-1L + 5L Reorder the terms: l = 5L + -3n-1x-1 + x-1L
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